# physics

#### Jimkeller1993

hi everyone, i am currently doing a degree in mechanical engineering and i am currently struggling with an assignment.

Basically we did an experiment where a roller disc was rolled down 2 rails and we had to calculate how long it takes to get from one end to the other, it was raised at 10cm increments each time and obviously the higher the gradient the quicker it got to the bottom.

we then have to calculate things such as radius of gyration, kinetic energy, potential energy and kinetic energy of rotation. now in one of the tables there is values given as S (m) - this is the distance of the rails
t (s) - Time in seconds
v (m/s) - velocity
v^2 (m/s^2) - ?
h (m) - height

i am also given a statement that says
the final linear velocity v is found from s = 1/2(u+v)t
now i have transposed this to 2s/t - u = v but how do i find v^2?

#### skeeter

Math Team
$v^2 = \left(\dfrac{2s}{t}-u\right)^2$

should be rather simple, espescially if initial velocity, $u=0$

#### Jimkeller1993

so thats all i have to do? maybe i looked a bit too in depth into it.
also once plotting a graph with with height on the vertical axis and v^2 on the horizontal how would i find the value of (h/v^2)?

#### skeeter

Math Team
$\dfrac{h}{v^2}$ would be the slope of the graph ...

#### Jimkeller1993

and how do i find that?
this is the first physics topic we have done and its certainly not my strongest subject

#### skeeter

Math Team
I would start by plotting a data graph of $h$ vs $v^2$ ...

1 person

#### Jimkeller1993

yes i have plotted the graph, i just dont know how to find the gradient

#### skeeter

Math Team
Have you constructed a line of best fit to your data? The data should follow a linear pattern.

#### Jimkeller1993

yes the line of best fit is a linear pattern

#### skeeter

Math Team
yes the line of best fit is a linear pattern
Then measure the slope ... $\dfrac{rise}{run}$, remember?